10/13/2016 QUESTIONS ON THE HOMEWORK, JUST ASK AND YOU WILL BE REWARDED THE ANSWER

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1 QUESTIONS ON THE HOMEWORK, JUST ASK AND YOU WILL BE REWARDED THE ANSWER 1

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4 CONTINUING WITH DESCRIPTIVE STATS 6E,6F,6G,6H,6I MEASURING THE SPREAD OF DATA: 6F othink about this example: Suppose you are at a high school football game and you sample 40 people from the student section about their age. othen you head to a professional game and you sample 40 random people there. You find that you have the same mean as the high school game. owhat is different about the two scenarios? oare they a good representation of the data collected? ophilosophical chair activity. 4

5 PHILOSOPHICAL CHAIR ACTIVITY. If you agree with the statement, then move to the Einstein wall (your right) If you disagree with the statement, move to the record side of the wall (your left). NO NEUTRALS, so own your opinion. After you choose a side, be ready to argue the point. The speaker has the blazer bear they must choose a rebuttal from the other side. If someone changes your mind/opinion, move to the other side immediately. This happens often. Ready? Stand up! Statement number 1: Any music censorship is wrong. STATEMENT 2: Fatty food should cost more money. 5

6 STATEMENT 3: Homework is an essential part of my learning. MATH STATEMENT #4 Data that has an outlier is flawed. 6

7 MATH STATEMENT #5 Learning to do things by hand that a calculator can do, isn t very important. MATH STATEMENT #6 Students greatly benefit from writing in their math class. 7

8 AN INTERESTING ONE: Teachers should not interact with students through social networking. MATH QUESTION #7 Is it possible to count past infinity? Left yes. Right no. = < ω < ω + 1 < ε 0 < θ 8

9 MONTY HALL PROBLEM Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice stay, or does it matter? Switchers go to the left, Stayers to the right. Back, it doesn t matter. SWITCH = 2 3 chance of winning DISPERSION osometimes mean, median and mode don t give you an accurate description of the distribution. To do that, we need to measure both the centre and its dispersion. owe can identify the centre, but the spread of the data can be analyzed 3 different ways: orange, ointerquartile range, ostandard deviation. 9

10 RANGE The range of the data, or the max minus the min is not a particularly reliable measure of spread. Why do you think that would be true? THE QUARTILES AND THE INTERQUARTILE RANGE The median divides the data into two even halves. If we look at the middle of the lower half, we have found the 1 st quartile, or the lower quartile. If we look at the middle of the upper half, we have found the 3 rd quartile, or the upper quartile. The distance between the two quartiles is called the Interquartile range. The tells us the range of the middle 50% of the data. IQR = Q 3 Q 1 10

11 EXAMPLE 1) Reorder the set 2) Find the median 3) Find the lower quartile and upper quartile. If there is a middle term, disregard it when finding the quartiles. If there are 2 terms for the median, use the lower one for Q 1 and the upper on for Q 3. 4) Calculate the IQR CALCULATOR EXAMPLE Use a GDC to calculate the Range, Q 1 & Q 3, and IQR. 11

12 6G BOX AND WHISKER PLOT Hopefully you have seen these before. Lets break it down Quickly. Make sure that you use a number line that is in increments. Why would that need to be true? WHAT WOULD A B&W LOOK LIKE IF DRAW AN EXAMPLE! Where on the number line is the outlier? Toward the positive side = positively skewed Toward the negative side = negatively skewed The data was a symmetrical distribution? The data was positively skewed? The data was negatively skewed? 12

13 OYO: TRY IT Create a box and whisker plot (boxplot) from the data: 13, 24, 14, 11, 9, 31, 33, 33, 33, 18, 29, 28 Use of a calculator can be helpful but it doesn t label the important values for you, so PARALLEL BOXPLOTS Simply put, two sets of data are compared on the same number line with two boxplots. Example: A hospital is trialing a new anesthetic drug and has collected data on how long the new and old drugs take before the patient becomes unconscious. They wish to know which drug acts faster and which is more reliable. Old drug times (s): 8, 12, 9, 8, 16, 10, 14, 7, 5, 21, 13, 10, 8, 10, 11, 8, 11, 9, 11, 14 New drug times (s): 8, 12, 7, 8, 12, 11, 9, 8, 10, 8, 10, 9, 12, 8, 8, 7, 10, 7, 9, 9 Lets put these on the same number line and compare the data. Use a 5-number summary! 13

14 PARALLEL BOXPLOTS Old drug times (s): 8, 12, 9, 8, 16, 10, 14, 7, 5, 21, 13, 10, 8, 10, 11, 8, 11, 9, 11, 14 New drug times (s): 8, 12, 7, 8, 12, 11, 9, 8, 10, 8, 10, 9, 12, 8, 8, 7, 10, 7, 9, 9 Faster? Reliable? INTERESTING TO NOTE Old drug times (s): 8, 12, 9, 8, 16, 10, 14, 7, 5, 21, 13, 10, 8, 10, 11, 8, 11, 9, 11, 14 Are any of these outliers? 14